A000694 Related to population of numbers of form x^2 + y^2. (Formerly M1021 N0384)

1, 2, 4, 6, 11, 19, 34, 63, 117, 218, 411, 780, 1487, 2849, 5477, 10562, 20419, 39563, 76805, 149360, 290896, 567321, 1107775, 2165487, 4237384, 8299283, 16268639, 31915437, 62656158, 123088460, 241958676, 475901501, 936544684

Offset

1,2

Comments

Shanks' paper gives erroneous value a(16)=10555. - Sean A. Irvine, Feb 25 2011

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..33.

D. Shanks, The second-order term in the asymptotic expansion of B(x), Mathematics of Computation 18 (1964), pp. 75-86.

Index entries for sequences related to populations of quadratic forms

Maple

Digits:=500;
K:=.764223653589220662990698731250092328116790541393409514721686673
7496146416587328588384015050131312337219372691207925926341874206467
8084323063315434629380531605171169636177508819961243824994277683469
0516235139218719620569053295644670419176349770659569905712938660289
3858998296105166296089099177929836072973697200640316985128636517347
3921065768550978681981674707359066921;
a:=n->round(evalf((2/3)*K*int(1/sqrt(ln(t)), t=1..2^n)));
# Sean A. Irvine, Feb 25 2011

Crossrefs

Cf. A000691.

Sequence in context: A048239 A000786 A289080 * A164137 A018170 A113913

Adjacent sequences: A000691 A000692 A000693 * A000695 A000696 A000697

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Feb 24 2011

Status

approved